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Hi Rita,
Thank you for posting your question in the Microsoft Q&A forum!
In general, there are recipient rate limit (10,000 recipients per day) and message rate limit (30 messages per minute) for Exchange Online mailbox. Does the problematic mailbox receive any NDR message that mentioned what kind of limitation this mailbox reached?
You can check this article for more details about O365 sending limits:
Also, if this specific user account is used for some third-party application and bulk-mailing scenarios, option 2 (SMTP relay) and 3 (Direct Send) is recommended instead in the following article:
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